MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Circular Kinematics

Two spherical...

Question

Two spherical conductors $A_{1}$ and $A_{2}$ of radii $r_{1}$ and $r_{2} (r_{2} > r_{1})$ are placed concentrically in air. $A_{1}$ is given a charge +Q while $A_{2}$ is earthed. Then the equivalent capacitance of the system is:

A

\frac{4 π ϵ_{0} r_{1} r_{2}}{r_{2} - r_{1}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

4 π ϵ_{0} (r_{1} + r_{2})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

4 π ϵ_{0} r_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

4 π ϵ_{0} r_{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{4 π ϵ_{0} r_{1} r_{2}}{r_{2} - r_{1}}$
By Gauss's law the electric field at a distance r in between the shells is
$E .4 π r^{2} = \frac{Q}{ϵ_{0}} \Rightarrow E = \frac{Q}{4 π ϵ_{0} r^{2}}$
The potential difference between shells is $\int_{0}^{V} d V = - \int_{r_{2}}^{r_{1}} E d r$
or $V = - \frac{Q}{4 π ϵ_{0}} \int_{r_{2}}^{r_{1}} \frac{d r}{r^{2}} = \frac{Q}{4 π ϵ_{0}} (\frac{1}{r_{1}} - \frac{1}{r_{2}})$
or $V = \frac{Q}{4 π ϵ_{0}} . \frac{r_{2} - r_{1}}{r_{1} r_{2}}$
$∴$ Capacitance, $C = \frac{Q}{V} = \frac{4 π ϵ_{0} r_{1} r_{2}}{r_{2} - r_{1}}$

Suggest Corrections

thumbs-up

1

Similar questions

Q. Two spherical conductors

A_{1}

A_{2}

r_{1}

r_{2}

and carrying charges

q_{1}

q_{2}

are connected in air by a copper wire as shown in the figure. Then the equivalent capacitance of the system is:

Q. A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig.). Show that the capacitance of a spherical capacitor is given by

c = \frac{4 π ϵ_{0} r_{1} r_{2}}{r_{1} - r_{2}}

r_{1}

r_{2}

are the radii of outer and inner spheres, respectively.

Q. Two spherical conductors A and B of radii a and b (b > a) are placed concentrically in air. B is given charge +Q and A is earthed. The equivalent capacitance of the system is :

Q. A metallic sphere of radius

R_{1}

+ Q

is nested inside a metallic spherical shell that has radius

R_{2}

Q

.
Which of the following changes will increase the capacitance of the system?
I: Increase the magnitude of the charge,

Q

R_{2}

R_{1}

R_{1}

R_{2}

IV: Increase both R1 and R2 while leaving the difference in radii,

R_{2} - R_{1}

Q. The mutual inductance between two planar concentric rings of radii

r_{1}

r_{2}

r_{1} >> r_{2}

) placed in air is given by

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Charge Motion in a Magnetic Field

PHYSICS

Watch in App

explore_more_icon

Explore more

Circular Kinematics

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon